Abstract
A distributed parameter linear model is derived from simplified physical equations of one dimensional open channel hydraulics. This linear model relating downstream to upstream flow rates is then identified analytically to a second order transfer function with delay, that can be used for controller synthesis. Analytical formulas for exact sampling with zero and first order holds are also given for the discrete-time case. The modelling error made when considering linear models around different reference discharges in a given set can be evaluated with a bound on multiplicative and on additive uncertainties. These bounds are useful for controller robustness analysis and synthesis.
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